Resolutions of co-letterplace ideals and generalizations of Bier spheres
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- by Alessio D’Alì, Gunnar Fløystad and Amin Nematbakhsh PDF
- Trans. Amer. Math. Soc. 371 (2019), 8733-8753 Request permission
Abstract:
We give the resolutions of co-letterplace ideals of posets in a completely explicit, very simple form. This generalizes and simplifies a number of linear resolutions in the literature, among them the Eliahou-Kervaire resolutions of strongly stable ideals generated in a single degree. Our method is based on a general result of K. Yanagawa using the canonical module of a Cohen-Macaulay Stanley-Reisner ring. We discuss in detail how the canonical module may effectively be computed and from this derive directly the resolutions.
A surprising consequence is that we obtain a large class of simplicial spheres comprehensively generalizing Bier spheres.
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Additional Information
- Alessio D’Alì
- Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- Address at time of publication: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
- MR Author ID: 1111831
- Email: alessio.d-ali@warwick.ac.uk
- Gunnar Fløystad
- Affiliation: Universitetet i Bergen, Matematisk institutt, Postboks 7803, 5020 Bergen, Norway
- Email: gunnar@mi.uib.no
- Amin Nematbakhsh
- Affiliation: School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
- MR Author ID: 1145179
- Email: nematbakhsh@ipm.ir
- Received by editor(s): March 21, 2017
- Received by editor(s) in revised form: January 11, 2018, February 13, 2018, and February 19, 2018
- Published electronically: March 28, 2019
- Additional Notes: Much of this work was carried out while the first and third authors were visiting the second author at the University of Bergen.
The third author received support from both the University of Bergen and the Institute for Research in Fundamental Sciences (IPM) during his stay. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8733-8753
- MSC (2010): Primary 13D02, 05E40; Secondary 52B55
- DOI: https://doi.org/10.1090/tran/7560
- MathSciNet review: 3955562